On atriodic tree-like continua

Oversteegen, Lex G.; Tymchatyn, E. D.

doi:10.1090/S0002-9939-1981-0620013-2

On atriodic tree-like continua
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by Lex G. Oversteegen and E. D. Tymchatyn

Proc. Amer. Math. Soc. 83 (1981), 201-204

DOI: https://doi.org/10.1090/S0002-9939-1981-0620013-2

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Abstract:

D. P. Bellamy has recently shown that atriodic tree-like continua do not have the fixed point property for homeomorphisms. J. B. Fugate and T. B. McLean showed that hereditarily indecomposable tree-like continua have the fixed point property for pointwise periodic homeomorphisms. In this paper the latter result is extended to the case of atriodic tree-like continua. In the course of the proof it is shown that the property of being an atriodic tree-like continuum is a Whitney property. In particular, it is shown that the hyperspace of an atriodic tree-like continuum is at most $2$-dimensional.

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